At level 30, you get an extra ranked option in the usual blind pick/draft mode column. Before going into ranked, you have to have atleast 16 champions including free week champions or it wont allow you to play ranked. This is 16 because if the 6 bans + 10 picks. If by coincidence the 6 bans + 9 other picks were champions you have, you'd still have one champion to choose.
To gain/lose elo is through dodging champion selects, and winning/losing games. Beware of the first 10 ranked games because those games are about +/- 50 elo compared to the normal +/- 10 to 15 elo.
The ranked win/lose ratio shows up after your first game. You just look at your profile and it should be there. However you wont see your elo until after a couple games